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Math Help - Reflecting Telescope

  1. #1
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    Reflecting Telescope

    A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep, where will the collected light be concentrated?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep (ähemm! are you sure?) , where will the collected light be concentrated?
    I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

    The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

    The general equation of a parabola opening to the right is:

    y^2 = 2p\cdot x

    Use the coordinates of P to calculate p. (I've got p = \frac23)

    Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates F\left(\frac p2\ ,\ 0\right)
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  3. #3
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    ok....

    Quote Originally Posted by earboth View Post
    I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

    The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

    The general equation of a parabola opening to the right is:

    y^2 = 2p\cdot x

    Use the coordinates of P to calculate p. (I've got p = \frac23)

    Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates F\left(\frac p2\ ,\ 0\right)
    Another great and helpful reply.
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